Understand what Venn Diagram is. Click on the link to Watch the VIDEOexplanation:
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Explanation of Venn Diagrams
As we know this is a Venn diagram. It is a visual presentation of sets. We have learnt about the union of sets and the intersection of sets. This can be diagrammatically represented by using a rectangle and circles or ellipces. The rectangle is used to represent a universal set while circle and ellipces represent the subsets of universal set.
To make this clear we consider an example. Here the universal set represents a collection of objects in a classroom, desk, bench, book, chair, duster and chalk piece. Set A contains a chalk piece, a duster and a chair. Notice that set A is a subset of the given universal set.
Set U is equal to desk, bench, book, chair, duster, chalk piece .
Set A is equal to chalk piece, duster, chair.
Now this can be represented in a Venn diagram. The rectangle represents the universal set. The circle representing the subset A contains a chalk piece, a duster and a chair while the desk, the book and the bench which are part of the universal set are all present outside the circle but inside the rectangle. Similarly we can use the Venn diagrams to represent the union and intersection of sets.
Let us consider the objects owned by two friends Mahesh and Ganesh. Mahesh has a dining table, a dressing table, a sofa set, a radio and a television represented by Set X. Ganesh has a dressing table, a radio, a cot and a computer represented by Set Y. Set X and Set Y have the dressing table and the radio in common.
Click on the Venn diagram button to view the representation of the sets in a Venn diagram.
Venn diagrams can also be used to find the cardinal number of a set. Let us consider an example and learn to find the cardinal number of a set using a Venn diagram.
A florist had 100 garlands of which 35 were garland with only jasmine flowers, 42 were garlands with only roses and the remaining garlands were a combination of both flowers. He wants to know the number of garlands that had both jasmine and rose. Shall we try to help him in finding the solution?
The number of garlands which had only jasmine is equal to 35. The number of garlands which had only rose is equal to 42. The total number of garlands is equal to 100. Therefore, the number of garlands having both rose and jasmine is equal to total number of garlands minus number garlands containing only jasmine added to the number of garlands containing only rose. That is equal to 100 minus 35 plus 42.
Therefore, the number of garlands containing both jasmine and rose is 23.
Let us consider an another example. Out of 8o students in a class 35 play cricket, 20 play football and 15 play both cricket and football. The class teacher wants to know the number of students who play neither cricket nor football. Shall we help the teacher find the number?
The total number of students in the class is equal to 80. The number of students who play cricket only is equal to the number of students who play cricket 35 minus the number of students who play both 15 that is equal to 20. Similarly the number of students who play only football is equal to the number of students who play football 20 minus the number of students play both 15 that is equal to 5. Therefore the number of students who neither play cricket nor football is equal to n of Set U minus n of C plus n of F plus n of C intersection F is equal to 80 minus 20 plus 5 plus 15 that is equal to 80 minus 40 that is equal to 40.
Watch Video
Explanation of Venn Diagrams
As we know this is a Venn diagram. It is a visual presentation of sets. We have learnt about the union of sets and the intersection of sets. This can be diagrammatically represented by using a rectangle and circles or ellipces. The rectangle is used to represent a universal set while circle and ellipces represent the subsets of universal set.
To make this clear we consider an example. Here the universal set represents a collection of objects in a classroom, desk, bench, book, chair, duster and chalk piece. Set A contains a chalk piece, a duster and a chair. Notice that set A is a subset of the given universal set.
Set U is equal to desk, bench, book, chair, duster, chalk piece .
Set A is equal to chalk piece, duster, chair.
Now this can be represented in a Venn diagram. The rectangle represents the universal set. The circle representing the subset A contains a chalk piece, a duster and a chair while the desk, the book and the bench which are part of the universal set are all present outside the circle but inside the rectangle. Similarly we can use the Venn diagrams to represent the union and intersection of sets.
Let us consider the objects owned by two friends Mahesh and Ganesh. Mahesh has a dining table, a dressing table, a sofa set, a radio and a television represented by Set X. Ganesh has a dressing table, a radio, a cot and a computer represented by Set Y. Set X and Set Y have the dressing table and the radio in common.
Click on the Venn diagram button to view the representation of the sets in a Venn diagram.
Venn diagrams can also be used to find the cardinal number of a set. Let us consider an example and learn to find the cardinal number of a set using a Venn diagram.
A florist had 100 garlands of which 35 were garland with only jasmine flowers, 42 were garlands with only roses and the remaining garlands were a combination of both flowers. He wants to know the number of garlands that had both jasmine and rose. Shall we try to help him in finding the solution?
The number of garlands which had only jasmine is equal to 35. The number of garlands which had only rose is equal to 42. The total number of garlands is equal to 100. Therefore, the number of garlands having both rose and jasmine is equal to total number of garlands minus number garlands containing only jasmine added to the number of garlands containing only rose. That is equal to 100 minus 35 plus 42.
Therefore, the number of garlands containing both jasmine and rose is 23.
Let us consider an another example. Out of 8o students in a class 35 play cricket, 20 play football and 15 play both cricket and football. The class teacher wants to know the number of students who play neither cricket nor football. Shall we help the teacher find the number?
The total number of students in the class is equal to 80. The number of students who play cricket only is equal to the number of students who play cricket 35 minus the number of students who play both 15 that is equal to 20. Similarly the number of students who play only football is equal to the number of students who play football 20 minus the number of students play both 15 that is equal to 5. Therefore the number of students who neither play cricket nor football is equal to n of Set U minus n of C plus n of F plus n of C intersection F is equal to 80 minus 20 plus 5 plus 15 that is equal to 80 minus 40 that is equal to 40.
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